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- The Chebyshev pseudospectral method for optimal control problems is based on Chebyshev polynomials of the first kind. It is part of the larger theory of pseudospectral optimal control, a term coined by Ross. Unlike the Legendre pseudospectral method, the Chebyshev pseudospectral (PS) method does not immediately offer high-accuracy quadrature solutions. Consequently, two different versions of the method have been proposed: one by Elnagar et al., and another by Fahroo and Ross. The two versions differ in their quadrature techniques. The Fahroo–Ross method is more commonly used today due to the ease in implementation of the Clenshaw–Curtis quadrature technique (in contrast to Elnagar–Kazemi's cell-averaging method). In 2008, Trefethen showed that the Clenshaw–Curtis method was nearly as accurate as Gauss quadrature. This breakthrough result opened the door for a covector mapping theorem for Chebyshev PS methods. A complete mathematical theory for Chebyshev PS methods was finally developed in 2009 by Gong, Ross and Fahroo. (en)
- 切比雪夫擬譜法（Chebyshev pseudospectral method）是以切比雪夫多项式為基礎的最优控制方法，是所創的擬譜最佳控制理論中的一部份。切比雪夫擬譜法和勒壤得擬譜法不同，無法立刻提供高精度的積分解。因此有二種從切比雪夫擬譜法衍生的技術，一個是Elnagar等人所提出的，另一個則是Fahroo和Ross所提出的。這兩種方式的差異是其求積的技術。現今Ross–Fahroo擬譜法較常使用，因為比較容易實現，比Elnagar–Kazemi的欄元平均法（cell-averaging method）要容易。Trefethen在2008年證明Clenshaw–Curtis求積法幾乎和高斯求积一樣的準確。這個突破性的結果開啟了針對切比雪夫擬譜法的伴隨向量映射原理研究。有關切比雪夫擬譜法的完整數學原理已在2009年由Gong、Ross及Fahroo所提出。 (zh)
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- 切比雪夫擬譜法（Chebyshev pseudospectral method）是以切比雪夫多项式為基礎的最优控制方法，是所創的擬譜最佳控制理論中的一部份。切比雪夫擬譜法和勒壤得擬譜法不同，無法立刻提供高精度的積分解。因此有二種從切比雪夫擬譜法衍生的技術，一個是Elnagar等人所提出的，另一個則是Fahroo和Ross所提出的。這兩種方式的差異是其求積的技術。現今Ross–Fahroo擬譜法較常使用，因為比較容易實現，比Elnagar–Kazemi的欄元平均法（cell-averaging method）要容易。Trefethen在2008年證明Clenshaw–Curtis求積法幾乎和高斯求积一樣的準確。這個突破性的結果開啟了針對切比雪夫擬譜法的伴隨向量映射原理研究。有關切比雪夫擬譜法的完整數學原理已在2009年由Gong、Ross及Fahroo所提出。 (zh)
- The Chebyshev pseudospectral method for optimal control problems is based on Chebyshev polynomials of the first kind. It is part of the larger theory of pseudospectral optimal control, a term coined by Ross. Unlike the Legendre pseudospectral method, the Chebyshev pseudospectral (PS) method does not immediately offer high-accuracy quadrature solutions. Consequently, two different versions of the method have been proposed: one by Elnagar et al., and another by Fahroo and Ross. The two versions differ in their quadrature techniques. The Fahroo–Ross method is more commonly used today due to the ease in implementation of the Clenshaw–Curtis quadrature technique (in contrast to Elnagar–Kazemi's cell-averaging method). In 2008, Trefethen showed that the Clenshaw–Curtis method was nearly as accur (en)
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- Chebyshev pseudospectral method (en)
- 切比雪夫擬譜法 (zh)
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